rotate text around its center in pycairo

At least on the version of cairo available on my machine (1.8.8), the following approach works for me:

def text(ctx, string, pos, theta = 0.0, face = 'Georgia', font_size = 18):
    ctx.save()

    # build up an appropriate font
    ctx.select_font_face(face , cairo.FONT_SLANT_NORMAL, cairo.FONT_WEIGHT_NORMAL)
    ctx.set_font_size(font_size)
    fascent, fdescent, fheight, fxadvance, fyadvance = ctx.font_extents()
    x_off, y_off, tw, th = ctx.text_extents(string)[:4]
    nx = -tw/2.0
    ny = fheight/2

    ctx.translate(pos[0], pos[1])
    ctx.rotate(theta)
    ctx.translate(nx, ny)
    ctx.move_to(0,0)
    ctx.show_text(string)
    ctx.restore()

Which can be used in the following way:

width = 500
height = 500
surface = cairo.ImageSurface(cairo.FORMAT_RGB24, width, height)
ctx = cairo.Context(surface)
ctx.set_source_rgb(1,1,1)
rect(ctx, (0,0), (width, height), stroke=False)
ctx.set_source_rgb(0,0,0)
for i in xrange(5):
    for j in xrange(5):
        x = 100 * i + 20
        y = 100 * j + 20
        theta = math.pi*0.25*(5*i+j)
        text(ctx, 'hello world', (x, y), theta, font_size=15)
surface.write_to_png('text-demo.png')

OK so cairo allows for text move_to and rotate. This means that what you want is to figure out (x,y) for move_to (T), such that when you rotate (R), the center point of your text is at your desired location, c=(cx,cy):

So you have to solve the equation Mv = c, where v is the text center relative to the text origin:

M = T*R

T = (1 0 x)
    (0 1 y)
    (0 0 1)

R =  (cos r    -sin r   0)
     (sin r     cos r   0)
     (0            0    1)

v = (w/2, h', 1)

c = (cx, cy, 1)

h' = h/2 - (h - y_bearing)

Sanity checks:

• when r is 0 (no rotation), you get x=cx-w/2, y=cy-h', which you know is the correct answer
• when r=-90 (text sideways, with "up" towards the right), you get what you expect, ie x = cx - h' and y = cy + w/2

For python code, you will have to rewrite the above equation so you end up with A*t=b, where t=(x,y), and you will compute t = inv(A)*b. Then, you will simply do

cr.move_to(x, y)
cr.rotate(r)
cr.show_text(yourtext)

Note that the coordinate system in cairo has +y going down so there will be a couple signs to fix, and maybe y_bearing is not correct, but you get the idea.